The Field of the Invention
The present invention pertains a one-return wave equation migration to extrapolate both down-going and up-going waves. Followed by properly designed imaging conditions, the partial images contributed from turning waves and multiple reflections are correctly reconstructed. Numerical examples show that this method can significantly enhance the imaging of an overhanging salt boundary and vertical faults.
The Prior Art
Conventional one-way wave equation migration has been successfully and widely applied to 3D pre-stack depth imaging for years. This method recursively downward continues source and receiver wavefields independently. It handles primary reflections but ignores the turning waves that propagate beyond 90° and multiple reflections, such as duplex waves that describe propagation paths with a double reflection involving a reflecting base boundary and a near vertical feature. It fails to produce good images of the geologic structure that contains strong turning waves and duplex waves, such as an overhanging salt boundary and geological structure with steep dip. Based on the two-way hyperbolic wave equation, reverse-time migration propagates the source wavefield forward and the receiver wavefields backward in time. Reverse-time migration has no dip limitation and also images most wave types, including turning waves and duplex waves. A properly designed imaging condition is critical to suppress the artifacts in prestack reverse-time migration. However, it is computationally expensive in that it demands huge storage and memory capabilities for large 3D datasets.
The Kirchhoff migration can handle the turning waves. Ratcliff et al. used the Kirchhoff integral method for imaging salt structures in the Gulf of Mexico (“Seismic Imaging of Salt Structures In the Gulf of Mexico,” The Leading Edge 11(4), 15-31, 1992). Reverse-time migration (Baysal, et al, “Reverse Time Migration,” Geophysics 48(11), 1514-1524, 1983; Biondi et al., Prestack “Imaging of Overturned Reflections by Reverse Time Migration”, Expanded Abstracts, SEG 72nd Annual Meeting 1284-1287, 2002) takes into account the turning waves, but it is usually computationally too expensive for practical applications.
One-way wave equation migration has been successfully and widely applied to 3D pre-stack depth imaging for years (O'Brien et al, “Wave Equation Pre SDM Advances Subsalt Imaging”, Offshore March, 2002, 36-40). Traditional one-way wave equation migration recursively downward continues source and receiver wave fields independently. It ignores the waves that propagate beyond 90°, stated as evanescent energy. In fact, the evanescent energy propagates upward and is received by geophones at the surface. Especially for those areas with a significant velocity gradient along depth, this part of energy can be record as the turning waves.
Claerbout (“Imaging the Earth's Interior,” Blackwell Scientific Publications, 1985, p. 272-273) proposed a two-pass phase shift, post-stack time migration for imaging turning waves. Since turning waves have abnormal moveout that degrades the images quality after normal move and (NMO) stack, this method has not been widely practiced. Hale et al., (“Imaging Salt Substructures With Turning Seismic Waves,” Geophysics, 57(11), 1453-1462, 1992) extended Claerbout's algorithm by pre-computing and tabulating phase shifts as a function of depth and reflection slope to avoid the upward-pass continuation. They also demonstrated how to preserve turning waves during stacking of seismic data to make the algorithm more useful.
Another option to migrate turning waves using one-way propagators is to extrapolate wave field along horizontal (Zhang J. et al, “Turning Wave Migration by Horizontal Extrapolation,” Geophysics 62(1), 291-296, 1997) or tilted coordinates (Shan G. et al, “Imaging Overturned Waves by Plane-Wave Migration in Titled Coordinates,” Expanded Abstracts, SEG 73nd Annual Meeting, 1067-1070, 2004; and Crawley et al, “DSR Wave-Equation Migration for Steep and Overturned Events,” Expanded Abstracts, SEG 75th Annual Meeting, 2005). The implementation based on this strategy is complicated for 3D cases. Also the lateral velocity variations tend to be stronger at the subsurface image point in the new coordinates.
The approach proposed is an extension of Claerbout's method based on the following aspects: Extend from post-stack time migration to prestack depth migration to avoid loss of turning waves in the stack stage; Use more accurate propagators, such as generalized screen propagators (GSP) (Jin, S., Wu, R. S. et al, “Prestack Depth Migration Using a Hybrid Pseudo-Screen Propagator,” Expanded Abstracts, SEQ 68th Annual Meeting, 1819-1822, 1998; Jin and Walraven, “Wave Equation GSP Prestack Depth Migration and Illumination,” The Leading Edge, 22, 604-610, 2003) and velocity-adaptive-coordinate-transform VAVT (Xu, S. et al, “One-way Wavefield Extrapolation Via Velocity Adaptive Coordinate Transform,” Expanded Abstracts, SEG 73rd Annual Meeting, 1067-1070, 2003) instead of phase-shift, to handle steep deeps with strong lateral velocity variations; and Design a specific imaging condition to obtain the image volumes contributed from different wave patterns.
U.S. Pat. No. 5,138,584 to Hale describes a method for migrating seismic data for formations that are located in geological media that cause seismic waves to be refracted so substantially that the waves turn upward. The method includes the steps of tabulating a first phase shift function as a function of the wave vector and the angular frequency of seismic waves in the geological media, tabulating a second phase shift function, storing the tabulated values of the first and second phase shift functions, calculating a third phase shift function based upon the first and second phase shift functions; and migrating recorded seismic data using the first, second and third phase shift functions.
U.S. Pat. No. 5,274,605 to Hill describes a process for depth migration of seismic wave information that has been derived from geological media that causes rapid lateral velocity variations in seismic waves. The process includes the step of decomposing waves fields recorded at the earth's surface using Gaussian beams as basic functions. Then, according to the process, the set of Gaussian beams is extrapolated downward into the earth to obtain the subsurface wave field. Finally, the wave field is processed to provide depth-migated images of subsurface reflectors.
U.S. Pat. No. 5,490,120 to Li et al describe an overturned wave identified in initial seismic data and revised seismic data gathering parameters are calculated (e.g., a range of locations for a seismic source and detectors laterally displaced from the source). The gathered seismic data is used to image the interface by using an imaging algorithm capable of migrating down going and upcoming reflections.
U.S. Pat. No. 5,530,679 to Albertin describes an approximation method for imaging seismic data that originates from steeply dipping or overturned strata. The method provides a viable alternate approach to the generalized f-k migration that does not relay explicitly on some form of pertubation series expansion and thus avoids the steep-dip instability that is present in previously-known methods. This method is particularly useful in the presence of a moderate lateral velocity gradient, something that prior-art methods have trouble accommodating. An advantageous feature of the disclosed method is that the migration/imaging operators are composed of simple numerical coefficients.
Duplex waves describe propagation paths with a double reflection involving a reflecting base boundary and a near vertical feature (Marmalyeyskyy, et al., “Migration of Duplex Waves,” Expanded Abstracts, SEG 75th Annual Meeting, 2005. Duplex waves exist in the geologic structure with vertical features such as faults and flank of salt bodies. In this case, primary reflections may not be recorded in a limited acquisition aperture. Therefore, one-way wave equation migration cannot produce the image of such events. Instead, doubly reflected duplex waves are recorded and should be taken into account in the migration. Migration of duplex waves can be conducted by Kirchhoff method. Marmalyeyskyy et al (2005) showed impressive results for imaging of the steep salt dome boundary and vertical fault. Due to the high frequency asymptotic approximation, the Kirchhoff method, however, has fundamental limitations in producing good subsurface images in complex media. Based on the concept of multiple fore-scattering, single back-scattering (MFSB) in heterogeneous medium, the present method uses a one-return wave equation migration that downward and upward extrapolates both down-going and up-going waves. Followed by a properly designed imaging condition, one-return migration produces the depth image of primary reflections that is same as conventional one-way equation migration as well as the image from the contribution of turning waves and duplex waves that one-way methods fail to handle.